1. Field of the Invention
The present invention relates generally to separating and measuring particles (including molecules) (e.g., in gases [aerosols] or in liquids [colloids or suspensions]), and in particular, to using a cross-flow differential migration classifier to separate and/or measure particles.
2. Description of the Related Art
The need to separate and measure particles (e.g., particles contained in gases [aerosols] [also referred to as atmospheric ultrafine particles] or in liquids [colloids or suspensions]) according to size or other parameters spans a wide range of science and technology. Many different separation/measurement techniques have been developed, but each suffers serious drawbacks and limitations, particularly in the domain of continuous separations. For example, prior art separation techniques are limited in their ability to provide/separate a high percentage of the total desired particles in a sample or to provide/separate particles within a desired size range. Such problems may be better understood by describing prior art separation techniques.
The ability to extract particles within a narrow interval of property values may enable measurements of the characteristics of a particulate system. For example, particle size distribution characteristics may be measured/determined by a detector that measures the number of mass of particles contained within a sample of classified/separated particles. In another example, a chemical analysis system may be employed as a detector to measure the composition distribution with respect to size. A detection system capable of determining the number or activity of particles of biological origin may enable pathogen detection. Further, a suitable separation system may enable preparations of bulk quantities of separated/classified materials for a wide range of applications.
As described above, a number of different separation/measurement techniques have been developed for particles contained in gases (aerosols) or liquids (colloids or suspensions), but each suffers serious drawbacks and limitations. Common prior art techniques that may measure particles are a condensation particle counter (CPC) and a differential mobility analyzer (DMA). A CPC may be used to determine the number concentration of particles larger than a critical size (e.g., 2.5 to 15 nm) but with a limited resolution of the particle size distribution. A DMA may enable size distribution measurements for particles in the submicron size range. By combining a DMA with a particle detector, such as the CPC, and stepping through a sequence of particle sizes, the combination may measure particle size distributions in a matter of minutes. By eliminating the delays between steps by scanning through particle size, measurements may be accelerated in a system that may be referred to as the scanning mobility particle sizer (SMPS™) or scanning electrical mobility spectrometer (SEMS).
A differential mobility analyzer (DMA) as illustrated in FIG. 1 is a classifier for charged particles contained in a gas (i.e., it sorts particles with respect to their electrical mobilities—a parameter that can be related to the particle size). A DMA is often used to sort/measure sub-micrometer aerosol particles according to size while keeping them suspended in air. First an electric charge is applied to the aerosol particles. In this regard, it is difficult to put more than one charge on small particles and as a result, most of the particles will either be uncharged or have a single charge. In the common implementations, although negatively charged particles can be classified by reversing the polarity on the DMA, only the positively charged particles are sorted by the DMA, all others may be lost.
After charging, the aerosol sample flow 102 containing the charged particles (referred to as polydisperse) are introduced into the DMA containing an electric field. In this regard, the electric field is created by two electrodes (e.g., center rod 104 and wall(s) 106A and 106B). The center rod 104 may be an inner cylinder that is connected to a negative power supply. The charged particles 102 are introduced close to one of the electrodes (e.g., walls 106A and 106B), while a larger flow of clean, particle free gas 108 (referred to as sheath air) is introduced to fill the remaining gap.
The particles within the DMA are allowed to migrate into the clean sheath air flow 108 under the influence of the electric field. Accordingly, the electric field applied between the two electrodes 104 and 106A/106B causes the charged particles of the appropriate polarity to migrate toward the electrode 104 on the clean-gas side of the flow channel. In this regard, particles with negative charge may be repelled towards and deposited on the outer wall(s) 106A/106B. Similarly, particles with a positive charge may migrate towards the negatively charged center rod 104. The rate of migration depends on the electrical mobility of the particles. Mobility in turn, depends on both the size and electrical charge of the particle. If all of the particles have the same charge, then particles of a given mobility are the same size. Since the particles migrate at different rates, they are spread out through the sheath air 108 according to mobility. In this regard, withdrawing a portion of the sheath air flow 108 separates a narrow range of particle mobilities from the rest of the aerosol 102.
At a downstream position, a classified-sample flow 110 (also referred to as monodisperse aerosol) is extracted from the clean gas side of the channel. The classified-sample flow 110 contains those particles that migrated across the channel during the time required for flow from the entrance port to the classified-sample extraction port, but that did not strike, and adhere to either the clean-side electrode 104 or the wall(s) 106A/106B. The uncharged particles exit the DMA with the excess air 112. Thus, the particles are separated according to electrical mobility, which is defined as the migration velocity per unit of applied field strength.
Thus, as described above, a small monodisperse aerosol flow 110 drawn through a slot in the center electrode 104 downstream from the sample 102 entrance slot extracts those particles that migrate across the gap in the time required to flow down the length of the column of the DMA. Particles of higher or lower mobilities either deposit on the walls of the classifier or are discharged with the major flow 112 passing between the electrodes 104 and 106A/106B and bypassing the sample 110 extraction slot.
DMA separation can be performed at a constant applied field strength or a time-varying applied field strength (i.e., the charge between electrodes 104 and 106A/106B may be constant or vary over time). When the field is constant, a steady-flow of mobility classified particles may be contained in the classified sample flow 110. In this regard, classified particle samples may be prepared for a wide-range of applications, including calibration of particle measurement instruments, measurements of mobility (or size) dependent properties, and direct applications of particles with tightly controlled properties. In a time-varying application, the mobility of the particles varies with time. Thus, the distribution of particles within the sampled aerosol 102 with respect to the particle mobility may be rapidly measured.
Given knowledge of the relationship between the particle mobility and size, measurements taken in a DMA can be translated into a high-resolution particle size distribution. The ability to resolve particle mobility in this method is determined by the ratio of the clean sheath gas 108 flow rate to the flow rate of the entering aerosol 102 flow. The throughput of classified particles 110 is determined by the product of the number of concentration of particles of appropriate size, the volumetric flow rate of the incoming aerosol 102, and the probability that an entering aerosol particle 102 will carry the appropriate charge.
Thus, the ability of the DMA to separate particles of different mobilities is determined by the ratio of the sum of the incoming aerosol and outgoing classified sample volumetric flowrates to the sum of the sheath and exhaust flows, i.e.,   β  =                    Q        a            +              Q        c                            Q        sh            +              Q        e            and the tendency of particles to diffuse away from their mean trajectory. Considering the conventional DMA designs in which the distance in the streamwise direction is large compared to the distance between electrodes 104 and 106A/106B, and noting that the particle diffusivities are generally small, diffusion in the cross-stream direction dominates.
The variance in the cross-stream position of the particles due to Brownian diffusion is:σ2=2Dtwhere D is the Brownian diffusivity of the particles. Thus, the relative variation in the cross-stream location upon migration across the gap (separation distance b) between electrodes 104 and 106A/106B at the average migration time (τmig=b/vmig) becomes:             σ      b        =                            2          ⁢          D                          b          ⁢                                           ⁢                      v                          m              ⁢                                                           ⁢              i              ⁢                                                           ⁢              g                                            ,where vmig=ZE is the migration velocity of a particle of electrical mobility Z, and E is the applied electric field strength. The dimensionless quantity bvmig/D describes the relative importance of transport by electrophoretic migration to that by Brownian diffusion. It has the form of a Peclet number, and has been labeled by migration Peclet number, Pemig=bvmig/D.
The diffusivity and electrical mobility can both be related to the mechanical mobility of the particle (B, the ratio of the terminal migration velocity to the applied force that causes the particle to migrate), i.e.,D=BkTZ=qB,where k is the Boltzmann constant, T is the temperature, and q is the charge on the particle. The electric field can be written as:       E    =                  Φ        b            ⁢              f        ⁡                  (          geometry          )                      ,where the dimensionless function of the geometry, ƒ(geometry), accounts for any nonuniformities in the electric field across the gap between the electrodes 104 and 106A/106B, Φis the applied voltage difference between the electrodes 104 and 106A/106B, and b is the separation distance between the electrodes 104 and 106A/106B.
Thus, the standard deviation in the cross-stream position after the mean migration time is:             σ      b        ≈                            2          ⁢                                           ⁢          k          ⁢                                           ⁢          T                          q          ⁢                                           ⁢          Φ                      =            2              P        ⁢                                   ⁢                  e                      m            ⁢                                                   ⁢            i            ⁢                                                   ⁢            g                              
The ability of a DMA to resolve small differences in particle mobilities can be characterized in terms of the ratio of the characteristic mobility of the particles that are transmitted to the breadth of the mobility range that is actually transmitted. Specifically, the resolving power or resolution may be defined at the mobility of the particles that are transmitted with the highest probability to the difference in mobilities between the highest and lowest mobilities that are transmitted with one-half of that probability. In the limit of nondiffusive particles, the resolution is:
 Rnd=β−1.
For highly diffusive particles, the resolution may scale as:       R    d    =            f      ⁡              (        geometry        )              ⁢          Φ              1        2            Thus, at high operating voltages, the relative amounts of particle-laden and particle-free flows determines the resolution, while at low voltages, it is the operating voltage that determines the resolution. For a number of existing differential mobility analyzers, the differences in performance of the ideal instruments is small, although nonidealities in instrument design and construction may lead to dramatic differences in the performance in the high voltage limit.
Various techniques have attempted to improve the limiting resolution. For example, in one technique, reducing the length to gap ratio to near unity may optimize the performance of the DMA design at a fixed Re. Such an approach may achieve modest improvements in the geometry factor in             R      d        =                  f        ⁡                  (          geometry          )                    ⁢              V                  1          2                      ,while maximizing the operating voltage, thereby maximizing Pemig, i.e., the approach is equivalent to maximizing Pemig while recognizing the constraints that must be imposed on the flow Reynolds number to avoid deleterious turbulence.
In another technique, the imposition of an electric field in the DMA column in the streamwise direction may increase the resolution beyond that predicted by the simple analysis described above. Further, the incorporation of inclined grids within the classification region may be a viable way to realize some gains. Also, substantial improvements in resolution at a given voltage may be achieved by appropriate use of nonuniform electric fields. Specifically, the DMA resolution may be enhanced by inducing migration from the inner electrode to the outer one in a cylindrical DMA. Both approaches have the potential to improve resolution beyond the limits suggested, although practical implementations have not yet been demonstrated.
Gains may also be maximized by reducing the radius of the inner electrode relative to that of the outer one in a cylindrical DMA. Further, gains may also be maximized by causing the particles to migrate across the DMA with no streamwise separation between the aerosol inlet and outlet ports.
In view of the above, to produce an unambiguous relationship between the particle mobility and the particle size, most applications of the DMA charge the particles by exposure to an ambipolar mixture of positive and negative gas ions (e.g., produced by exposure to a radioisotope or produced by corona discharge). As described above, under typical ambient conditions, charging particles in this manner may result in a small fraction of particles carrying a single charge. Of the singly charged particles, approximately one-half will possess appropriate polarity for classification, further reducing the fraction of sampled particles that will be included in the classified-sample flow 110.
While this prior art approach has the advantage of producing a well-characterized charge distribution, the approach results in most particles within a size range of interest being lost within the classification region. In this regard, when particles are above a certain size (e.g., 100 nm) and in typical ambient temperature and pressure air, the number of particles carrying multiple charges becomes substantial. As the particle size further increases (e.g., beyond 1 μm in diameter), multiple charging is so substantial that the prior art approach is rarely extended beyond such particle sizes.
Alternate charging approaches have been employed to increase the fraction of small particles charged or to produce a more consistent relationship between the mobility of super-micron particles and the particle size. Regardless of the charging method employed, the aerosol 102 flow rate through the DMA may be limited by the need to maintain laminar flow (e.g., to efficiently separate/classify the particles). Such limitations therefore limit the value of prior art DMAs in the preparation of quantities of classified particles for scientific or technological applications. The transition from laminar to turbulant flow may be evaluated and/or determined by the flow Reynolds number:       Re    =                  ρ        ⁢                                   ⁢        U        ⁢                                   ⁢        L            μ        ,where ρ is the density, U is the velocity, L is the characteristic length of the flow system, and μ is the viscosity.
The Reynolds number must be kept below a critical value to maintain laminar flow. The clean sheath gas 108 flow through the DMA must be larger than the aerosol sample 102 flow to achieve high mobility/size resolution. Accordingly, the flow of aerosol 102 that can be processed is only a small fraction of that which might be processed through the channel in the absence of the sheath flow 108. Since the product of the characteristic length scale (L) of the device and the gas velocity (U) determines the magnitude of the Reynolds number, there is a severe constraint on the throughput of the DMA.
Prior art DMAs have not generally been applied to the classification of particles in liquid for a number of reasons. The presence of a fluid phase that is of comparable density to the particles drastically alters the forces of interaction between the particles and the wall(s) 106A/106B of the classifier. For particles in gases, van der Waals forces are sufficiently strong that once a particle reaches a wall 106A/106B, it adheres strongly. With liquids, the van der Waals forces are weaker. Additionally, molecular interactions may even cause particles to be repelled from the wall. However, in either gases or liquids, particles may continue to move along the wall(s) 106A/106B to be included in the classified sample flow, although clever flow designs could enable the wall layer to be removed prior to extracting the classified-sample flow 110.
During the separation of particles using a DMA, cross-flow mobility fractionation may be observed. In other words, the particles are separated based on their ability to migrate which provides fractionation in cross-flow like patterns within the DMA channel. However, instead of cross-flow mobility fractionation, the separation of particles in liquids has taken advantage of the ability of particles to continue to migrate even in close proximity to a surface. For example, a technique that takes advantage of such an ability is referred to as Field Flow Fractionation (FFF) as illustrated in FIGS. 2A and 2B. In FFF, particles 102 are passed in a laminar flow through a narrow channel 200 between appropriate surfaces 202A and 202B. The laminar flow produces a parabolic velocity profile 204, with the streamwise velocity peaking at the center of the channel 200 and dropping to zero near the walls 202A and 202B.
Brownian diffusion causes the particles 102 to migrate randomly across the narrow channel 200. While in the center of the channel 200, particles 102 are carried down the channel 200 at high velocities. However, when the particles 102 are near the wall(s) 202A/202B, the particles move down the channel 200 at much lower velocities. If a field 206 (e.g., gravity, electrical, magnetic, etc.) is applied perpendicular to the direction of flow, particles 102 may be pushed near the wall 202B. Brownian diffusion enables particles to sample different regions of the flow, although the time that different particles will spend in different regions will depend on their diffusivities and on the forces that the applied field applies to them. Thus, a pulse of particles 102 having a range of diffusivities that are introduced into the channel 200 flow will separate in time as they are carried down the channel 200.
A bias in the position of the particles 102 within the flow channel 200 can also be affected by introducing or extracting a flow through one or both walls (e.g., wall 202A or 202B). This technique is called flow Field Flow Fractionation (fFFF). fFFF is capable of separating colloidal particles over sizes ranging from nanometers to many micrometers, and with quite high resolution. A transverse field 206 (i.e., parallel to the surfaces but perpendicular to the direction of flow) can in some cases enable continuous separation.
Thus, as described above, in FFF, the transit time of particles down a narrow channel 200 varies according to the extent to which different particles sample the flow within the channel 200. A field 206 applied across the narrow dimension of the channel drives particles toward one surface (e.g., wall 202B) where the streamwise velocity is low.
An additional variant of FFF referred to as SPLITT (split flow thin fractionation) may also be used to separate particles continuously. In SPLITT, the flow channel has a carrier inlet, a sample inlet, and two outlets. The applied field causes particles to migrate to different regions of the flow so that the flow may be separated into the two outlet streams. The result provides a coarse separation into two fractions—one with particles larger than a given size, and the other with smaller particles. Multiple splitters may also be used to increase the number of fractions. However, the number of fractions may remain small and the range of migration velocities included in any fraction may remain relatively large.
Various other methods have been used to measure ultrafine particle size distributions. For example, the electrical aerosol analyzer was a predecessor to the DMA, with far more limited size resolution and sensitivity. A diffusion battery uses a CPC to count particles that pass through a screen or capillary on which the smaller particles deposit by Brownian diffusion. By using a range of such diffusional barriers, the diffusion battery can be used to determine particle size distribution. However, the particle size distribution may be determined with a resolution that is lower than that of SMPS. Cascade impactors may separate aerosol particles into discrete fractions that are collected on a substrate. A relatively new configuration that does enable continuous measurements is the electrical low pressure impactor (ELPI). In this instrument, the particles may be charged before introduction into the impactor. The deposited current provides an indication of the numbers of particles collected on the various impaction stages.
As described above, the CPC may be used to determine the concentration of particles larger than a critical size. To perform such a determination, the CPC condenses a vapor on the particles to grow them to a size that is easily detected optically, typically greater than 1 μm in diameter. The resulting large particles can be counted with near 100% efficiency. The absolute counting efficiency of the CPC is determined by the extent to which the particles are lost by Brownian diffusion to surfaces prior to growth, and by the efficiency of activation. The surface tension of a liquid increases the vapor pressure over a small droplet, so that there is a minimum particle size that can be activated at a given supersaturation. The smallest particles activated by commercially available CPCs range from 2.5 to about 15 nm diameter, depending on the working fluid employed and the difference in temperatures between the vapor source and the condenser regions of the instrument. This sensitivity to supersaturation has been used to achieve limited size resolution in CPC measurements.
Parallel CPCs operated at different supersaturations to detect particles larger than different threshold sizes may also be employed. For example, modest size resolution from a single CPC may be obtained by analyzing the intensity of light scattered by droplets grown on particles that are close to the threshold for activation.
In view of the above, what is needed is a method, apparatus, and article of manufacture for continuously separating particles of varying sizes where the classified-sample flow 110 constitutes a higher percentage of the total flow 102 entering a fractionator/DMA and is a larger flow than that of the prior art.